1. Field of the Invention
The present invention relates to a method for estimating parameters of a navigation signal which is received by a receiver which receives navigation signals through a plurality of paths wherein the parameters include data modulated on the navigation signal and complex amplitudes, e.g. amplitude and phase shift, and time delays of the individual paths.
2. Description of the Prior Art
Estimation of signal parameters (in particular delay and phase) of signals, which are transmitted by signal transmitters of known position to the receiver allow for position determination of the receiver within the three-dimensional space, insofar as within a synchronous system wherein the receiver clock is synchronized to the clocks of the transmit stations at least the signals of three transmitting station can be received. When the receiver clock is not synchronized to the clocks of the transmit stations, it is required to receive at least the signals of four transmit stations simultaneously, as in addition to the three spatial coordinates of the receiver position also the clock error of the receiver has to be estimated. The described method of positioning is commonly termed Time-of-Arrival (TOA) or pseudoranging and is used by satellite navigation systems for instance. If beside the delay estimate also the phase estimates are used the method is termed carrier phase positioning.
Considering a two-dimensional scenario for instance the delay estimates yield circles around the transmitters in the position domain, whereas their intersections indicate possible positions of the receiver as illustrated in FIG. 1. In practice some of the intersection points can be disregarded due to prior knowledge, such that a non-ambiguous solution exists. Analogously to the two-dimensional problem in a three-dimensional scenario the delay estimates are represented by spheres in the position domain, whereas the center points of each sphere are the transmit stations respectively.
A major problem for the TOA method are errors of the respective delay and phase estimates, which result in errors of the position estimate. Commonly for obtaining the delay estimates the delay-lock-loop (DLL) and for obtaining the phase estimates a phase-lock-loop (PLL) is used. The key idea is to have a method available, which is able to outperform the conventional DLL+PLL architecture with respect to the quality of the signal parameter estimates delay and phase. As the uncertainty within the signal parameter estimates is transformed into an uncertainty of the position estimate a further objective is to handover a complete probability density function for the signal parameters over to the position estimation, which is restricted to a Gaussian density for the conventional DLL+PLL architecture.
DLL as well as PLL are simple tracking loops. The DLL approximates a sequential estimator for the delay using an iterative gradient method which keeps track of the cross-correlation peak of a receiver reference signal and the received signal. The derivative of the correlation function is approximated by differencing the correlation values obtained by two reference signals that are delayed by τ0+0.5Δ and in advance by τ0−0.5Δ (early and late correlators) with respect to assumed maximum at τ0. Thereby Δ is termed the correlator spacing. Via a control loop that controls the velocity of the reference signals using a voltage or number controlled oscillator (VCO/NCO) the DLL adjusts the VCO/NCO such that the derivate of the correlation function becomes zero, which is equivalent to having the so called inphase correlator at τ0 perfectly synchronized to the received signal (see FIG. 2).
Within the state of the art approach it is assumed that the errors of the delay estimate are affected by a Gaussian error, whereas the variance of the error depends upon a set of parameters: bandwidth of the received signal, signal-to-noise ratio, correlator spacing Δ, period of coherent correlation/integration, loop filter characteristics.
The inphase signal corresponding to a delay of τ0 is provided to the PLL, which carries out the phase estimation similarly to the DLL by using a control loop (FIG. 3). The error of the phase estimates is commonly considered to be also Gaussian.
Disadvantages of State of the Art Approach
The estimation errors of the DLL and PLL are considered to be Gaussian today, such that the associated likelihood function for the estimates is consequently also a Gaussian. Actually the likelihood function is not a Gaussian and the conventional approach is not able to consider this.
In addition the DLL adjusts the derivative of the correlation function such that it becomes zero. This method is suboptimal due to the approximation of the derivative and it is known that the delay can be estimated better, if the approximation becomes more accurate. Practically this is achieved by decreasing the correlator spacing Δ, which yields improved performance with respect to the estimation error for the delay. Anyhow decreased spacing Δ deteriorates the dynamic performance of the DLL and leads to an increased probability of loosing lock, such that a trade-off between the different performance criteria is required.